Potential buyers for Cox will have to pay between £300m and £400m, according to non-executive chairman Peter Owen.
Owen said the new Cox management would be actively looking at ways to grow the business. "But having said that, I can't say it won't be sold."
Owen also refuted claims, made in last weekend's The Sunday Times that the proposed Cox and Highway merger in April failed because the insurer was under-reserved by £70m.
"Highway's board made a presentation to us which included figures from their actuary EMB.
"They said we were under-reserved by £70m. We went through the presentation line by line and could find no truth in the claim.
"Actuary Bacon and Woodrow saw the figures and has not changed its view on our reserves."
According to sources, Direct Line and esure founder Peter Wood, who launched a takeover of Cox 18 months ago, wanted EMB to assess the books during negotiations, but Cox refused.
Last week, it is understood that two institutional shareholders on the Cox board, which control 30% of the company, convened a crisis meeting to replace Neil Utley with ex-Coutts chief Andrew Fisher. Sources said Utley was "stunned and shocked" at the news.
Owen said that the board had decided that the management team needed "to be refreshed with someone who had the sufficient skills toolkit to take the company forward. Andrew has those skills".
"This wasn't about Neil's inadequacies. After five and a half years of excellent work, Neil wanted a change."
Owen said Fisher would continue to look at "consolidation opportunities" .